Problem: Find all solutions to the equation $\!\sqrt{2-3z} = 9$.  Express your answer as a common fraction.
Solution: We square both sides to get rid of the square root sign.  This gives us $2-3z = 81$.  Solving for $z$ gives $z = \boxed{-\frac{79}{3}}$.  We squared an equation, so we have to test our solution to make sure it isn't extraneous.  We have \[\sqrt{2 - 3\left(-\frac{79}{3}\right)} =\sqrt{2+79} = 9,\]so our solution is valid.